Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;

public class main {
    public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public static PrintWriter pw = new PrintWriter(System.out);
    public static String line;
    public static StringTokenizer st;
    public static ArrayList<ArrayList<Integer>> adjList;
    public static int[] dx = {-1, 0, 1, 0, -1, 1, 1, -1};
    public static int[] dy = {0, 1, 0, -1, 1, 1, -1, -1};
    public static int INF = 0x3f3f3f3f;
    public static long LINF = 0x3f3f3f3f3f3f3f3fL;
    public static int MOD = 1000000007;

    public static int R, C;
    public static TreeSet<Integer> rows, cols;
    public static int[][] grid;
    public static ArrayList<String> out;

    public static void checkRows(){
        while(!rows.isEmpty()){
            int r = rows.first();
            boolean fin = false;
            for(int c = 0; c < C; c++){
                grid[r][c]--;
                if(grid[r][c] == 0){
                    if(rows.contains(r)) rows.remove(r);
                    if(cols.contains(c)) cols.remove(c);
                }
            }
            out.add("row " + (r+1));
        }
    }

    public static void checkCols(){
        while(!cols.isEmpty()){
            int c = cols.first();
            boolean fin = false;
            for(int r = 0; r < R; r++){
                grid[r][c]--;
                if(grid[r][c] == 0){
                    if(rows.contains(r)) rows.remove(r);
                    if(cols.contains(c)) cols.remove(c);
                }
            }
            out.add("col " + (c+1));
        }
    }

    public static void main(String[] args) throws Exception{
        st = new StringTokenizer(br.readLine());
        R = Integer.parseInt(st.nextToken());
        C = Integer.parseInt(st.nextToken());


        rows = new TreeSet<Integer>();
        cols = new TreeSet<Integer>();
        for(int i = 0; i < R; i++){
            rows.add(i);
        }
        for(int j = 0; j < C; j++){
            cols.add(j);
        }

        grid = new int[R][C];
        for(int i = 0; i < R; i++){
            st = new StringTokenizer(br.readLine());
            for(int j = 0; j < C; j++){
                grid[i][j] = Integer.parseInt(st.nextToken());
                if(grid[i][j] == 0){
                    if(rows.contains(i)) rows.remove(i);
                    if(cols.contains(j)) cols.remove(j);
                }
            }
        }
        out = new ArrayList<String>();

        if(R <= C){
            checkRows();
            checkCols();
        } else{
            checkCols();
            checkRows();
        }

        boolean f = true;
        for(int i = 0; i < R; i++){
            for(int j = 0; j < C; j++){
                if(grid[i][j] != 0){
                    f = false;
                }
            }
        }

        if(f){
            pw.print(out.size() + "\n");
            for(String s : out){
                pw.print(s + "\n");
            }
        } else{
            pw.print("-1\n");
        }

        pw.close(); 
        br.close();
    }
}